Murugan R
Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):011901. doi: 10.1103/PhysRevE.76.011901. Epub 2007 Jul 2.
We develop a generalized theory of the site-specific DNA-protein interactions, which includes both the static as well as the dynamical factors influencing the one-dimensional diffusion of the nonspecifically bound protein molecule which is in the process of searching for the specific site on the DNA lattice. We argue that the chemically driven condensation of the DNA molecule introduces a static distribution in the one-dimensional phenomenological diffusion coefficient associated with the protein molecule and the conformational dynamics of the DNA introduces temporal fluctuations in the one-dimensional diffusion coefficient over the static distribution. We further derive the generalized inequality conditions and the scaling laws which are required to enhance the three-dimensional diffusion controlled site-specific association rate to an arbitrary order. Our model predicts that when the degree of condensation of the DNA molecule under consideration is very high, then the probability distribution associated with the stationary state one-dimensional diffusion coefficient variable as well as the stationary state one-dimensional diffusion length variable will be a flat one. Further analysis reveals that to achieve a site-specific association rate which is higher than that of the three-dimensional diffusion controlled rate, the one-dimensional diffusion length associated with the dynamics of the nonspecifically bound protein molecule on the DNA lattice should fall in certain critical ranges. Comparison of our theoretical results with the recent experimental observations reveals that when the DNA molecule is under a stretched condition, then the static distribution of the one-dimensional diffusion coefficient associated with the dynamics of the protein molecule on the DNA lattice is a Gaussian and therefore the fluctuations in the one-dimensional diffusion coefficient generated by the dynamical factors are confined in a harmonic type potential.
我们发展了一种位点特异性DNA-蛋白质相互作用的广义理论，该理论既包括影响非特异性结合蛋白质分子一维扩散的静态因素，也包括动态因素，这种非特异性结合蛋白质分子正处于在DNA晶格上寻找特定位点的过程中。我们认为，DNA分子的化学驱动凝聚在与蛋白质分子相关的一维唯象扩散系数中引入了一种静态分布，而DNA的构象动力学在这种静态分布上引入了一维扩散系数的时间波动。我们进一步推导了将三维扩散控制的位点特异性缔合速率提高到任意阶数所需的广义不等式条件和标度律。我们的模型预测，当所考虑的DNA分子的凝聚程度非常高时，与稳态一维扩散系数变量以及稳态一维扩散长度变量相关的概率分布将是平坦的。进一步分析表明，要实现高于三维扩散控制速率的位点特异性缔合速率，与非特异性结合蛋白质分子在DNA晶格上的动力学相关的一维扩散长度应落在某些临界范围内。将我们的理论结果与最近的实验观察结果进行比较发现，当DNA分子处于拉伸状态时，与蛋白质分子在DNA晶格上的动力学相关的一维扩散系数的静态分布是高斯分布，因此由动态因素产生的一维扩散系数的波动被限制在一种谐振型势中。
